How can I vectorize this loop out of existence?
To set up my problem as generally as possible, A and B are matrices that have the same number of rows, say m. Otherwise they have arbitrary column size.
Let size(A, 2) = k, and size(B, 2) = l
The loop I want to vectorize.
for t = 1:m
ARP = ARP + A(t,:)' * B(t,:)
end
Which is a sum of matrices size (kX1)X(1Xl) = kXl.
Finally ARP = 1/m * ARP
After some research I built this 'solution' which balloons up the size of my matrices and in fact fails when the matrices get largish.
%Create copies of A stacked on top of each other to a depth of l
exA = repmat(A, l, 1); % (m * k)Xl
%Reshape it so that exA has each column of A cloned k times
exA = reshape(exA, m, k * l); % mX(k * l)
%Create copies of B stacked next to each other to a width k
exB = repmat(B, 1, k); % mX(l * k)
%Both matrices are now m X k*l so we can elementwise multiply
%and take the mean of the rows.
ARP = mean(exA .* exB, 1); % 1X(k * l)
ARP = reshape(ARP, l, k)';
I am also aware that repmat can be replaced in vectorizations with bsxfun, although it is not clear how to implement bsxfun in this case. I appreciate any help that gets me to an optimized solution and also illustrates techniques for vectorization that I can study for similar problems.
Thanks in advance Mike
